The only way you will find out is if you apply. however, if your only source of income is a state pension, then chances are that you will be declined.
The state income is what is classed as the minimum you need to survive - the obvious question is, how will you repay any amounts that you take on credit?
If you own your own home, and have always paid bills on time, then you may get a card, however, you may not.
Try applying to a company such as Capital One - they tend to be more 'generous' when it comes to underwriting.